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Pricing Method for Contingent Claim Based on Martingale and Linear Programming Dual Principle

Chongfeng Wu

Abstract

A kind of calculation method for the seller′s arbitrage price and the buyer′s arbitrage price of any contingent claim in finite security market is presented by applying linear programming dual principle, martingale measure theory and perfect hedging method. Following two cases are studied: (a) allowing short selling securities and allowing borrowing and lending cash; (b) not allowing short selling securities but allowing borrowing and lending cash. The analyses show that the arbitrage prices can be obtained by solving some corresponding linear programming problems in martingale measure′s spaces.

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Key concepts: Martingale (probability theory), Arbitrage, Linear programming, Mathematical economics, Measure (data warehouse), Dual (grammatical number), Martingale pricing, Security market